7.5.1

# Magnetic Flux Density

Test yourself

## Magnetic Force

Magnetic force is the attractive or repulsive force felt by a charge when it is moving in a magnetic field.

### Magnetic force

• Magnetic force can be calculated using the following equation:
• Force = charge x velocity x field strength x $sin({\theta})$
• $F=qvBsin({\theta})$
• Where ${\theta}$ is the angle between the velocity and the field lines.

### Magnetic field strength

• The magnetic field strength, B, is a measure of how dense the field lines are.
• The units of magnetic field strength are Tesla (T).

## Fleming's Left-Hand Rule

Fleming's left-hand rule is a useful way of telling which direction the field, the movement of the charge and the current flow in a magnetic field.

### Perpendicular directions

• The field, the movement of the charge and the current have to be in perpendicular directions, so they must all be at 90o to each other.
• If you hold your left hand as shown in the image:
• Your thumb represents the direction of movement of the charge.
• Your first finger represents the field.
• Your middle finger represents the current.

### Method

• The question will give you two out of three of these quantities.
• You will need to line up those fingers then see which direction the last one is pointing in.
• Remember field lines run from the north pole to the south.

## Magnetic Force on a Wire Experiment

We can investigate how the force on a wire varies with flux density, current and length of wire in the magnetic field by using a top pan balance.

### Apparatus

• Set up the apparatus as shown in the diagram.
• For this investigation, aim to make the angle of the wire with the field as close as possible to 90°.
• Caution: the current should not exceed 4A (as the variable resistor is likely to smoke).

### Variables to investigate

• Using the arrangement on the previous slide, we can investigate the magnitude of the force as a function of:
• Flux density of the magnetic field.
• Current in the wire.
• Length of wire in the field.
• Angle between wire and field lines.

### Formula for magnetic force

• The formula for the magnetic force is:
• $F=BIL\sin\theta$
• Where F is the force, B is the magnetic field strength, L is the length of wire in the field and θ is the angle between the field lines and the wire.

### Analysis example for current

• Plot a graph of force against current.
• The line of best fit should be a straight line that passes through the origin.
• By comparison with “y = mx + c”, the gradient of the line should be equal to $BL\sin\theta$.